The story here flows much, much better than last time. Whereas The Sorcerer's Stone was jumpy and jumbled as it flowed from start to finish, this movie feels more appropriately suited for film, and is much easier to sink into.
While The Sorcerer's Stone had some very dark moments, it retained a somewhat lighthearted tone that didn't always match the action. The Chamber of Secrets, however, manages to blend its tone and subject matter much better. While death was often mentioned in the previous film, here we actually see a bit of bloody on-screen violence.
The visual effects in this film are much better than in the last, but are still far from perfect. The Quidditch match is less embarassing to watch, but it's not great either. The spiders go back and forth from looking obviously fake to rather impressively realistic. The Basilisk itself looks near-perfect, but the difference between the CG model and the real-life animatronic model is very obvious. I'm actually not sure which model is inferior; it could be that the CG model doesn't correctly reflect light, or it could be that the fake skin on the animatronic model isn't as realistic as it should be. Either way, both models look amazing on their own; they're just distractingly different.
The acting in this film has also improved over the last one. The child actors are less awkward, and it helps a bit. Jason Isaacs' portrayal of Lucius Malfoy is masterful; he's the very model of a great villain.
This chapter in the Harry Potter series initially seems to be a self-contained adventure, where nothing is lost or gained, and everything merely returns to the status quo at the end. A singular evil rose, and Harry defeated it. Were someone to judge the entire series based on the first two books/films, they might assume that it was nothing more than a series of magical mystery stories for children, rather than what it truly is: a deeply-woven mythology filled with realistically developing characters and wonderful storytelling.
However, future Potter books/films refer back to The Chamber of Secrets, revealing how the specific events here are, in fact, of immense importance. Repeat viewings, in light of the sequels, are much more entertaining.
Honestly, there's not much to say about this film that wasn't already said about the first. The acting is better, the special effects are better, and the story gets a tad darker. Certain elements work extremely well in film form, notably the Basilisk battle and certain lines of well-said dialogue. These little bits of fun elevate the film above its predecessor, and set the bar just a bit higher for the series as a whole.